In this paper, the control volume method (CVM) with the staggered grid system is utilized to solve the two-dimensional Brinkman equation for different configurations of porous media in a horizontal channel. The values of the permeability of sand and clear fluid are considered when performing several numerical investigations which enable the evaluation of the behaviour of the flow through regions that mathematically model some geological features (faults/fractures) present in oil reservoirs or groundwater flows. We have found that the convergence of the CVM can be achieved within a reasonable number of iterations when there is a gap present between a partial barrier of low Darcy number and the channel boundary. However, a complete barrier across the channel results in a very high resistance and hence there is a large pressure drop which causes difficulties in convergence. In order to improve the rate of convergence in such situations, an average pressure correction (APC) technique, which is based on global mass conservation, is developed. The use of this technique, along with the CVM, can rapidly build up the pressure drop across such a barrier and hence dramatically improve the rate of convergence of the iterative scheme. Copyright (C) 2003 John Wiley Sons, Ltd.